A translation reference loop frequency synthesizer for generating an output signal with sub-Hz frequency steps over a full octave. The synthesizer has a phase lock loop circuit and a translation reference loop. The phase lock loop circuit generates a phase lock oscillator output signal based on a phase lock feedback signal and a phase lock reference signal. The translation reference loop generates the phase lock reference signal based on mixing a translation reference frequency signal and a translation reference loop divided signal. The translation reference loop includes a series of translation loop dividers for generating the translation reference loop divided signal by dividing a frequency of the phase lock oscillator output signal. The translation reference loop includes a translation reference frequency generator for generating the translation reference frequency signal.